Secluded Path via Shortest Path
نویسندگان
چکیده
We provide several new algorithmic results for the secluded path problem, specifically approximation and optimality results for the static algorithm of [3, 5], and an extension (h-Memory) of it based on de Bruijn graphs, when applied to bounded degree graphs and some other special graph classes which can model wireless communication and line-of-sight settings. Our primary result is that h-Memory is a PTAS for degree-∆ unweighted, undirected graphs, providing a ⌈√ ∆+1 h+1 ⌉ -approximation in time O(hn logn); in particular, 0-Memory (i.e., static) provides a √ ∆+ 1-approximation (i.e., = √ ∆+ 1 − 1), tightening the previous analysis of this algorithm, and ∆-Memory is optimal (i.e., = 0), and is faster than the known optimal algorithm for this setting [3]. We also show that 0-Memory and 1-Memory give constant approximations for unit-disk graphs and planar graphs, and that an extension of h-Memory solves many other tessellation graphs. Finally, we prove that the problem is NP-hard on node-weighted graphs of degree 3.
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